battery dying when the phone is off.

So My wife and I are up in international falls MN for the week, and I have been having a weird issue with my phone. The last few days it has been completely dying overnight. I still have a 3g signal when I turn it off before I go to bed. Last night I had 60% battery life, I turned it off and it was completely dead when I went to try to turn it back on in the morning. gps, wifi and all that stuff is turned off almost all the time so it's not that. WTF is going on?